Ramified class field theory and duality over finite fields

Rahul Gupta; Amalendu Krishna

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arXiv · 2104.03029

Ramified class field theory and duality over finite fields

Rahul Gupta·Amalendu Krishna

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Abstract

We prove a duality theorem for the $p$-adic etale motivic cohomology of a variety $U$ which is the complement of a divisor on a smooth projective variety over $\F_p$. This extends the duality theorems of Milne and Jannsen-Saito-Zhao. The duality introduces a filtration on $H^1_{\etl}(U, {\Q}/{\Z})$. We identify this filtration to the classically known Matsuda filtration when the reduced part of the divisor is smooth. We prove a reciprocity theorem for the idele class groups with modulus introduced by Kerz-Zhao and Rulling-Saito. As an application, we derive the failure of Nisnevich descent for Chow groups with modulus.

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BibTeX RIS

Rahul Gupta, Amalendu Krishna. 2021-04-07. Ramified class field theory and duality over finite fields. https://arxiv.org/abs/2104.03029

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